What does a confidence interval tell us and why is it importance to use a confidence interval?
Let's look at four defintions of confidence interval first:
-An interval formulated to have specific probability of containing the real value of an unknown parameter. A 95 percent confidence interval has a 95 percent probability of containing the parameter being estimated
-Means for stating numerically the level of confidence about a result
-A range of values to estimate a value of a population parameter. Associated with the range of values is also the amount of confidence the researcher has in the estimate. For example, we might estimate the cost of a new space vehicle to be 35 million dollars. Assume that the confidence level is 95% and the margin of error is 5 million dollars. We say that we are 95% confident that the cost is between 30 and 40 million dollars.
-A range around the sample estimate in which the population estimate is expected to fall with a specified degree of confidence, usually 95% of the time or 90% of the time.
What is the importance of using Confidence Intervals?
Statisticians stress the importance of using confidence intervals (CIs). There is, however, debate over which type of CIs to use and how to best define and interpret them. In spite of this confusion, you should use CIs to express the results of statistical tests because they convey more information than P values alone.
StatsDirect documentation uses the common (see below) ...
This solution exmaines what a confidence interval tell us and why it is importance to use a confidence interval.